1. Technical Field of the Invention
The present invention is directed to a partitioned aperture wavefront imaging system and a method for measuring amplitude and phase of a light field at a plane. Methods and systems according to the invention enable the production of high resolution images and the ability to reconstruct the light field at other planes displaced from the measurement plane.
2. Description of the Prior Art
Generally, to fully characterize a light field, one must measure the local amplitude and phase of the wavefront. If the light field is roughly collimated, the amplitude and phase vary slowly in space, and only a low spatial resolution measurement is necessary for a complete characterization of the wavefront, referred to as wavefront sensing. On the other hand, if the light field is not well collimated, such as the light field from an extended source, then a high resolution characterization becomes necessary. Such high resolution measurements are generally referred to as wavefront imaging. Wavefront sensors or imagers measure the phase and amplitude of a light field at a particular plane. This not only provides complete information of the light field at the measurement plane, but also enables the numerical reconstruction of the light field at other planes closer to or farther from the measurement plane. The measurement of light amplitude is straightforward. A standard camera (CCD, CMOS or other) is sensitive to the intensity of light, which is proportional to the amplitude squared. Thus, a camera directly provides an amplitude image. The measurement of phase is less straightforward.
However, there are many well-known techniques for imaging phase. For example, many common phase microscopes use either Zernike phase contrast (PC) techniques [1] or Nomarski differential interference contrast (DIC) techniques [2]. One variant if DIC is called PlasDIC, which is available from Carl Zeiss Microscopy, LLC, Thornwood, N.Y. However, these devices only provide non-quantitative images of wavefront phase, meaning that the absolute wavefront phase cannot be retrieved from a single PC or DIC image. PC and DIC microscopes differ in the type of images they produce. PC produces a direct phase image (albeit non-quantitative), whereas DIC produces a phase derivative image (also non-quantitative). Phase gradient images are perhaps more pleasing to the eye because they convey an impression of oblique illumination that gives the images the appearance of 3D relief. A variety of oblique illumination and/or detection techniques also provide phase gradient contrast, but these are also non-quantitative.
Standard Nomarski DIC and Zernike phase contrast (PC) are non-quantitative phase imaging techniques in the sense that it is not possible, from a single DIC or PC image, to distinguish phase from amplitude contributions in the image. It is thus not possible to reconstruct the physical attributes in a sample associated with phase (or amplitude). In contrast, quantitative phase imaging techniques distinguish phase from amplitude, and thus enable an accurate reconstruction of the physical attributes of an image sample associated with phase (examples of such attributes are index of refraction, dry mass, and optical path length).
The development of quantitative phase imaging techniques was largely initiated by the astrophysics community to solve the problem of atmospheric turbulence when imaging with telescopes. Specifically, phase fluctuations caused by atmospheric turbulence can be compensated by a technique called adaptive optics, which requires the use of a wavefront sensor (note: star light impinging a telescope is essentially collimated). The most common wavefront sensors are Shack-Hartmann (SH) sensors [3], which provide 2D phase gradient images. These are popular because they are quantitative, light efficient, exhibit a large dynamic range, and are achromatic. Moreover, fast numerical algorithms have been developed to rapidly convert phase gradient images into absolute (direct) phase images. However, while SH wavefront sensors exhibit exquisite phase resolution, they exhibit poor spatial resolution.
Strategies to combine quantitative phase imaging with high spatial resolution have come from multiple directions. For example, from the microscopy community, a variety of techniques have been developed to render phase imaging, (direct or gradient) quantitative. Examples of direct phase imaging technique usually involve some kind of interferometry with phase stepping. The interferometer reference phase can come from an external beam, as in phase-stepping digital holography (DH) [4], [5], or from a low-pass-filtered version of the wavefront itself, as in Fourier microscopy [6] or SLIM [7]. Alternatively, the interferometry can be in a shear geometry (e.g. qDIC [8], [9]), thus providing quantitative phase gradient imaging (as opposed to direct phase imaging). Variations are Spiral Phase (SP) microscopy, which makes use of a rotating spiral phase plate [10] to obtain phase stepping. A sequence of images with at least 3 phase steps must be acquired to obtain quantitative phase contrast, meaning that image acquisition speed is reduced by a factor of three, and imaging is sensitive to motion artifacts. Single-shot phase stepping can be obtained with off-axis interferometry, as in off-axis DH [11] [12] (the latter is marketed by LyncéeTecDHM) and iSLIM [13], at the cost of reduced spatial resolution. Alternatively, the three (or four) images can be projected simultaneously onto the camera, at the cost of reduced field of view (FOV) and/or resolution (e.g. [9], [14]—note: the latter technique uses polarization-based phase stepping).
As an alternative to interferometric approaches, oblique illumination or detection can also confer phase-gradient contrast (GF [15], DPC [16]). For example, in DPC two images are sequentially acquired with complementary half blocks in the illumination aperture. A subtraction of the two images thus provides phase gradient contrast in a single direction (x). A second pair of images with the orientation of the half blocks rotated 90 degrees leads to phase gradient contrast in the y direction, thus leading to 2D phase gradient contrast. An absolute phase image can then be obtained by an integration algorithm (to within an integration constant).
Another strategy for phase imaging is based on phase diversity. For example, when a sample is out of focus, phase contrast is revealed as intensity contrast. By acquiring a sequence of at least two images with different focus adjustments, a phase image can be numerical computed based on a variety of algorithms (e.g. [17]). Either the images are acquired sequentially with moving parts (e.g. [18]), or they are acquired simultaneously. For example, simultaneous acquisition can be achieved with two cameras at different focal planes (LyncéeTecDHM), or with the use of a color camera and a reliance on chromatic aberrations [19]. The numerical algorithms in these techniques are fairly sophisticated and sensitive to noise.
Yet another strategy for phase contrast imaging comes from revisiting the SH wavefront sensor. Phasics has marketed a variation of the SH wavefront sensor that provides higher spatial resolution though at the cost of reduced light efficiency and/or reduced dynamic range [20]. More recently, Lytro™ has introduced a new camera to the general public that enables focusing a posteriori after the photo has been taken. The Lytro camera is a plenoptic (or light-field) camera [21], which, essentially, is a SH wavefront sensor with higher spatial resolution. In effect, a plenoptic camera records both the wavefront amplitude and tilt (or phase). The amplitude is encoded in coarse pixel blocks (4×4 in the Lytro camera), whereas the tilt is encoded in the finer intensity variations within the pixel blocks. Note: the size of the pixel block defines the net plenoptic camera spatial resolution (the larger the block, the worse the resolution).